$$\begin{array}{l}v_{x}=v_{x}(x, y, z, t) \\v_{y}=v_{y}(x, y, z, t) \\v_{z}=v_{z}(x, y, z, t) \\p=p(x, y, z, t) \\\rho=\rho(x, y, z, t) \\T=T(x, y, z, t)\end{array}$$vx=vx(x,y,z,t)vy=vy(x,y,z,t)vz=vz(x,y,z,t)p=p(x,y,z,t)ρ=ρ(x,y,z,t)T=T(x,y,z,t)
$$\begin{array}{l}\rho q_{V}\left(\beta_{2} v_{2 a x}-\beta_{1} v_{1 a x}\right)=F_{f x}+F_{p_{n} x} \\\rho q_{V}\left(\beta_{2} v_{2 a y}-\beta_{1} v_{1 a y}\right)=F_{f y}+F_{p_{n} y} \\\rho q_{V}\left(\beta_{2} v_{2 a z}-\beta_{1} v_{1 a z}\right)=F_{f z}+F_{p_{n} z}\end{array}$$ρqV(β2v2ax−β1v1ax)=Ffx+FpnxρqV(β2v2ay−β1v1ay)=Ffy+FpnyρqV(β2v2az−β1v1az)=Ffz+Fpnz
假如有效截面上的密度与速度均为常量,$\beta=1$β=1,化简为
$$\begin{array}{l}\rho q_{V}\left( v_{2 a x}-_{1} v_{1 a x}\right)=F_{f x}+F_{p_{n} x} \\\rho q_{V}\left( v_{2 a y}- v_{1 a y}\right)=F_{f y}+F_{p_{n} y} \\\rho q_{V}\left( v_{2 a z}- v_{1 a z}\right)=F_{f z}+F_{p_{n} z}\end{array}$$ρqV(v2ax−1v1ax)=Ffx+FpnxρqV(v2ay−v1ay)=Ffy+FpnyρqV(v2az−v1az)=Ffz+Fpnz